What does problem-based math learning unlock for students? Part 1

Problem-based learning helps engage all students in math. This three-part series explains how—and how teachers can implement it in their classrooms.

By Amplify Staff | July 28, 2022

Webinar series recap, part 1 of 3

Problem-based math learning helps teachers set the stage for memorable learning experiences and transfer the responsibility for the learning to students, which has been shown to help develop students’ problem-solving and math reasoning skills.

Our webinar series explores how this type of instruction engages all students in grade-level math every day, and how instructors can go about implementing problem-based learning in the classroom. In part 1 of the webinar series, award-winning teacher Kristin Gray asks—and answers—the question: What does problem-based learning unlock for students?

Experience and explanation form a learning cycle

Imagine you’ve just gotten a new piece of technology: a phone, a TV, a computer. How do you learn to use it? Do you read the entire user guide first? Jump in and never touch the guide? Or turn it on and try some things, referencing the guide as needed? 

If the last option sounds like you, that’s very common—and it’s an example of learning through problem-solving. 

“It’s something we naturally do,” says Gray.  “We’ve had a phone before so we would pick up this new phone and try doing things that we know worked on our last phone, and then we would experiment: Does it work the same on this phone? This bouncing between experience and explanation is really the foundation of how we learn through problem-solving.”

What learning through problem-solving looks like in the math classroom

If we think of instructional methods in the math classroom along a spectrum, on one end we might have a classroom where students are left to solve a problem and discover the relevant math on their own. On the other end, the instructional method might be to show students how to get the answer and then practice doing similar problems. 

The methods at both extremes are challenging, and it’s hard for instructors to go from one to the other, says Gray. “We need to install a soft landing space in the middle of these extremes—and we can think of that space as learning through problem-solving, or problem-based learning.” 

What does that look like in the math classroom? 

Students will tackle interesting problems, raise questions about the math required, receive an explanation, and apply it back to the problem—as with the example of learning new technology. 

“When we show students how to get the answer, we send the message that math is solely about answer-getting and learning processes. Answers are important, but we want to use problems to teach the math, not just teach students to get the answer,” says Gray. 

Practice is also key, she adds: “This place in the middle pulls the best from both extremes and puts them into a structure that supports teachers in teaching and students in learning.”

Why students should learn through problem-solving

Learning through problem-solving has the potential to engage all learners in math, says Gray. It influences the way teachers and students think of themselves as mathematicians and what it means to know and do math. 

In the 2000 NAEP survey, 70 percent of fourth and eighth graders reported that they enjoy activities that challenge their thinking, and enjoy thinking about problems in new ways. 

“Students are already naturally curious and like solving challenges and trying things in new ways, so that’s a great start,” says Gray. 

“No matter how kindly, clearly, patiently, or slowly teachers explain, they cannot make students understand,” says Gray. “Understanding takes place in the student’s mind as they connect new information with previously developed ideas. Teachers can help, but understanding is a by-product of solving problems.” 

Add understanding is motivating. It inspires perseverance and confidence. It supports making connections, not learning concepts in isolation. 

When students are given a new problem and are able to use prior knowledge to help solve it, that “promotes the development of autonomous learners,” says Gray. 

How Amplify Math supports problem-based learning

Amplify Math supports teachers in the planning and delivery of problem-based lessons. It also enables teachers to monitor student progress and differentiate instruction based on real-time data. 

Lessons start with warm-ups that tap into prior knowledge and move into problems that require collaboration to solve. Teachers monitor, engage, and ultimately synthesize student work into the main idea. There are also ample opportunities for practice and reflection. 

Learn more about Amplify Desmos Math.

Register to watch the rest of the series here

Visit Gray’s site, Math Minds, here.

Mathematics Problem-based learning

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